<!DOCTYPE html><html lang="zh-CN" data-theme="light"><head><meta charset="UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width,initial-scale=1"><title>GCC自带的一些builtin内建函数 | Tom's develop Blog</title><meta name="keywords" content="GCC 内建函数"><meta name="author" content="Tom"><meta name="copyright" content="Tom"><meta name="format-detection" content="telephone=no"><meta name="theme-color" content="#ffffff"><meta http-equiv="Cache-Control" content="no-transform"><meta http-equiv="Cache-Control" content="no-siteapp"><meta name="description" content="一些GCC自带的内建(bulitin)函数的接口及实现">
<meta property="og:type" content="article">
<meta property="og:title" content="GCC自带的一些builtin内建函数">
<meta property="og:url" content="https://tomsworkspace.github.io/2021/02/27/GCC%E8%87%AA%E5%B8%A6%E7%9A%84%E4%B8%80%E4%BA%9Bbuiltin%E5%86%85%E5%BB%BA%E5%87%BD%E6%95%B0/index.html">
<meta property="og:site_name" content="Tom&#39;s develop Blog">
<meta property="og:description" content="一些GCC自带的内建(bulitin)函数的接口及实现">
<meta property="og:locale" content="zh_CN">
<meta property="og:image" content="https://cdn.jsdelivr.net/gh/TOMsworkspace/TOMsworkspace.github.io/2021/02/27/GCC自带的一些builtin内建函数/figure1.jpg">
<meta property="article:published_time" content="2021-02-27T10:57:00.000Z">
<meta property="article:modified_time" content="2021-02-27T12:08:46.863Z">
<meta property="article:author" content="Tom">
<meta property="article:tag" content="GCC">
<meta property="article:tag" content="bulitin函数">
<meta name="twitter:card" content="summary">
<meta name="twitter:image" content="https://cdn.jsdelivr.net/gh/TOMsworkspace/TOMsworkspace.github.io/2021/02/27/GCC自带的一些builtin内建函数/figure1.jpg"><link rel="shortcut icon" href="https://cdn.jsdelivr.net/gh/TOMsworkspace/BlogHelper@1.0/avatar.png"><link rel="canonical" href="https://tomsworkspace.github.io/2021/02/27/GCC%E8%87%AA%E5%B8%A6%E7%9A%84%E4%B8%80%E4%BA%9Bbuiltin%E5%86%85%E5%BB%BA%E5%87%BD%E6%95%B0/"><link rel="preconnect" href="//cdn.jsdelivr.net"/><link rel="preconnect" href="//busuanzi.ibruce.info"/><link rel="preconnect" href="//zz.bdstatic.com"/><link rel="stylesheet" href="/css/index.css"><link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/@fortawesome/fontawesome-free/css/all.min.css"><link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/@fancyapps/fancybox@latest/dist/jquery.fancybox.min.css"><script>var GLOBAL_CONFIG = { 
  root: '/',
  algolia: undefined,
  localSearch: undefined,
  translate: {"defaultEncoding":2,"translateDelay":0,"msgToTraditionalChinese":"繁","msgToSimplifiedChinese":"簡"},
  noticeOutdate: undefined,
  highlight: {"plugin":"highlighjs","highlightCopy":true,"highlightLang":true},
  copy: {
    success: '复制成功',
    error: '复制错误',
    noSupport: '浏览器不支持'
  },
  relativeDate: {
    homepage: false,
    post: false
  },
  runtime: '天',
  date_suffix: {
    just: '刚刚',
    min: '分钟前',
    hour: '小时前',
    day: '天前',
    month: '个月前'
  },
  copyright: {"limitCount":50,"languages":{"author":"作者: Tom","link":"链接: ","source":"来源: Tom's develop Blog","info":"著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。"}},
  ClickShowText: {"text":"富强,民主,文明,和谐,自由,平等,公正,法治,爱国,敬业,诚信,友善","fontSize":"15px"},
  lightbox: 'mediumZoom',
  Snackbar: undefined,
  justifiedGallery: {
    js: 'https://cdn.jsdelivr.net/npm/justifiedGallery/dist/js/jquery.justifiedGallery.min.js',
    css: 'https://cdn.jsdelivr.net/npm/justifiedGallery/dist/css/justifiedGallery.min.css'
  },
  isPhotoFigcaption: false,
  islazyload: true,
  isanchor: false
};

var saveToLocal = {
  set: function setWithExpiry(key, value, ttl) {
    const now = new Date()
    const expiryDay = ttl * 86400000
    const item = {
      value: value,
      expiry: now.getTime() + expiryDay,
    }
    localStorage.setItem(key, JSON.stringify(item))
  },

  get: function getWithExpiry(key) {
    const itemStr = localStorage.getItem(key)

    if (!itemStr) {
      return undefined
    }
    const item = JSON.parse(itemStr)
    const now = new Date()

    if (now.getTime() > item.expiry) {
      localStorage.removeItem(key)
      return undefined
    }
    return item.value
  }
}</script><script id="config_change">var GLOBAL_CONFIG_SITE = { 
  isPost: true,
  isHome: false,
  isHighlightShrink: false,
  isToc: true,
  postUpdate: '2021-02-27 20:08:46'
}</script><noscript><style type="text/css">
  #nav {
    opacity: 1
  }
  .justified-gallery img {
    opacity: 1
  }

  #recent-posts time,
  #post-meta time {
    display: inline !important
  }
</style></noscript><script>(function () {  window.activateDarkMode = function () {
    document.documentElement.setAttribute('data-theme', 'dark')
    if (document.querySelector('meta[name="theme-color"]') !== null) {
      document.querySelector('meta[name="theme-color"]').setAttribute('content', '#0d0d0d')
    }
  }
  window.activateLightMode = function () {
    document.documentElement.setAttribute('data-theme', 'light')
   if (document.querySelector('meta[name="theme-color"]') !== null) {
      document.querySelector('meta[name="theme-color"]').setAttribute('content', '#ffffff')
    }
  }
  const autoChangeMode = 'true'
  const t = saveToLocal.get('theme')
  if (autoChangeMode === '1') {
    const isDarkMode = window.matchMedia('(prefers-color-scheme: dark)').matches
    const isLightMode = window.matchMedia('(prefers-color-scheme: light)').matches
    const isNotSpecified = window.matchMedia('(prefers-color-scheme: no-preference)').matches
    const hasNoSupport = !isDarkMode && !isLightMode && !isNotSpecified
    if (t === undefined) {
      if (isLightMode) activateLightMode()
      else if (isDarkMode) activateDarkMode()
      else if (isNotSpecified || hasNoSupport) {
        const now = new Date()
        const hour = now.getHours()
        const isNight = hour <= 6 || hour >= 18
        isNight ? activateDarkMode() : activateLightMode()
      }
      window.matchMedia('(prefers-color-scheme: dark)').addListener(function (e) {
        if (saveToLocal.get('theme') === undefined) {
          e.matches ? activateDarkMode() : activateLightMode()
        }
      })
    } else if (t === 'light') activateLightMode()
    else activateDarkMode()
  } else if (autoChangeMode === '2') {
    const now = new Date()
    const hour = now.getHours()
    const isNight = hour <= 6 || hour >= 18
    if (t === undefined) isNight ? activateDarkMode() : activateLightMode()
    else if (t === 'light') activateLightMode()
    else activateDarkMode()
  } else {
    if (t === 'dark') activateDarkMode()
    else if (t === 'light') activateLightMode()
  }})()</script><meta name="generator" content="Hexo 5.2.0"></head><body><div id="sidebar"><div id="menu-mask"></div><div id="sidebar-menus"><div class="author-avatar"><img class="avatar-img" data-lazy-src="https://cdn.jsdelivr.net/gh/TOMsworkspace/BlogHelper@1.0/avator.jpg" onerror="onerror=null;src='/img/friend_404.gif'" alt="avatar"/></div><div class="site-data"><div class="data-item is-center"><div class="data-item-link"><a href="/archives/"><div class="headline">文章</div><div class="length-num">38</div></a></div></div><div class="data-item is-center"><div class="data-item-link"><a href="/tags/"><div class="headline">标签</div><div class="length-num">73</div></a></div></div><div class="data-item is-center"><div class="data-item-link"><a href="/categories/"><div class="headline">分类</div><div class="length-num">12</div></a></div></div></div><hr/><div class="menus_items"><div class="menus_item"><a class="site-page" href="/"><i class="fa-fw fas fa-home"></i><span> Home</span></a></div><div class="menus_item"><a class="site-page" href="/archives/"><i class="fa-fw fas fa-archive"></i><span> Archives</span></a></div><div class="menus_item"><a class="site-page" href="/tags/"><i class="fa-fw fas fa-tags"></i><span> Tags</span></a></div><div class="menus_item"><a class="site-page" href="/categories/"><i class="fa-fw fas fa-folder-open"></i><span> Categories</span></a></div><div class="menus_item"><a class="site-page" href="/link/"><i class="fa-fw fas fa-link"></i><span> Link</span></a></div><div class="menus_item"><a class="site-page" href="/about/"><i class="fa-fw fas fa-heart"></i><span> About</span></a></div></div></div></div><div id="body-wrap"><header class="post-bg" id="page-header" style="background-image: url(https://cdn.jsdelivr.net/gh/TOMsworkspace/TOMsworkspace.github.io/2021/02/27/GCC自带的一些builtin内建函数/figure1.jpg)"><nav id="nav"><span id="blog_name"><a id="site-name" href="/">Tom's develop Blog</a></span><span id="menus"><div class="menus_items"><div class="menus_item"><a class="site-page" href="/"><i class="fa-fw fas fa-home"></i><span> Home</span></a></div><div class="menus_item"><a class="site-page" href="/archives/"><i class="fa-fw fas fa-archive"></i><span> Archives</span></a></div><div class="menus_item"><a class="site-page" href="/tags/"><i class="fa-fw fas fa-tags"></i><span> Tags</span></a></div><div class="menus_item"><a class="site-page" href="/categories/"><i class="fa-fw fas fa-folder-open"></i><span> Categories</span></a></div><div class="menus_item"><a class="site-page" href="/link/"><i class="fa-fw fas fa-link"></i><span> Link</span></a></div><div class="menus_item"><a class="site-page" href="/about/"><i class="fa-fw fas fa-heart"></i><span> About</span></a></div></div><span class="close" id="toggle-menu"><a class="site-page"><i class="fas fa-bars fa-fw"></i></a></span></span></nav><div id="post-info"><h1 class="post-title">GCC自带的一些builtin内建函数</h1><div id="post-meta"><div class="meta-firstline"><span class="post-meta-date"><i class="far fa-calendar-alt fa-fw post-meta-icon"></i><span class="post-meta-label">发表于</span><time class="post-meta-date-created" datetime="2021-02-27T10:57:00.000Z" title="发表于 2021-02-27 18:57:00">2021-02-27</time><span class="post-meta-separator">|</span><i class="fas fa-history fa-fw post-meta-icon"></i><span class="post-meta-label">更新于</span><time class="post-meta-date-updated" datetime="2021-02-27T12:08:46.863Z" title="更新于 2021-02-27 20:08:46">2021-02-27</time></span><span class="post-meta-categories"><span class="post-meta-separator">|</span><i class="fas fa-inbox fa-fw post-meta-icon"></i><a class="post-meta-categories" href="/categories/GCC/">GCC</a></span></div><div class="meta-secondline"> <span class="post-meta-separator">|</span><span class="post-meta-wordcount"><i class="far fa-file-word fa-fw post-meta-icon"></i><span class="post-meta-label">字数总计:</span><span class="word-count">1.5k</span><span class="post-meta-separator">|</span><i class="far fa-clock fa-fw post-meta-icon"></i><span class="post-meta-label">阅读时长:</span><span>6分钟</span></span><span class="post-meta-separator">|</span><span class="post-meta-pv-cv"><i class="far fa-eye fa-fw post-meta-icon"></i><span class="post-meta-label">阅读量:</span><span id="busuanzi_value_page_pv"></span></span><span class="post-meta-separator">|</span><span class="post-meta-commentcount"><i class="far fa-comments fa-fw post-meta-icon"></i><span class="post-meta-label">评论数:</span><a href="/2021/02/27/GCC%E8%87%AA%E5%B8%A6%E7%9A%84%E4%B8%80%E4%BA%9Bbuiltin%E5%86%85%E5%BB%BA%E5%87%BD%E6%95%B0/#post-comment"><span class="gitalk-comment-count comment-count"></span></a></span></div></div></div></header><main class="layout" id="content-inner"><div id="post"><article class="post-content" id="article-container"><h2 id="一、GCC内建函数"><a href="#一、GCC内建函数" class="headerlink" title="一、GCC内建函数"></a>一、GCC内建函数</h2><p>&emsp;最近在刷 <a target="_blank" rel="noopener" href="https://leetcode-cn.com/">leetcode</a> 的时候遇到了一些以__builtin开头的函数，它们被用在状态压缩相关的题目中特别有用，于是就去了解了一下。</p>
<p>&emsp;原来这些函数是GCC编译器自带的内建函数。这些__builtin_*形式的内建函数一般是基于不同硬件平台采用专门的硬件指令实现的，因此性能较高。在刷题时可以直接用而不用重复造轮子，尤其是一些涉及到位操作的内建函数真的特别有用。</p>
<p>&emsp;我对其中涉及到位运算的内建函数挺感兴趣的，于是就去查了一下它们的接口以及具体实现。下一节主要介绍一下几个特别有用的函数。</p>
<p>&emsp;关于GCC内建函数的更完整的内容可以参见 <a target="_blank" rel="noopener" href="https://gcc.gnu.org/onlinedocs/gcc-4.3.2/gcc/Other-Builtins.html#Other-Builtins">官方文档</a>。</p>
<h2 id="二、常用的内建函数及实现"><a href="#二、常用的内建函数及实现" class="headerlink" title="二、常用的内建函数及实现"></a>二、常用的内建函数及实现</h2><p>&emsp;针对实现，只实现64位无符号整型的版本。其余的版本依此类推。</p>
<h3 id="1、-builtin-ctz"><a href="#1、-builtin-ctz" class="headerlink" title="1、__builtin_ctz"></a><strong>1、__builtin_ctz</strong></h3><p>&emsp;一共有三个函数，分别适用于不同的输入类型。</p>
<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_ctz (<span class="keyword">unsigned</span> <span class="keyword">int</span> x)</span><br><span class="line">Returns the number of trailing <span class="number">0</span>-bits in x, starting at the least significant bit position. If x is <span class="number">0</span>, the result is undefined.</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> __builtin_ctzl (<span class="keyword">unsigned</span> <span class="keyword">long</span>)</span><br><span class="line">Similar to __builtin_ctz, except the argument type is <span class="keyword">unsigned</span> <span class="keyword">long</span>.</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> __builtin_ctzll (<span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span>)</span><br><span class="line">Similar to __builtin_ctz, except the argument type is <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span>.</span><br></pre></td></tr></table></figure>
<p>&emsp;这个函数作用是返回输入数二进制表示从最低位开始(右起)的连续的0的个数；如果传入0则行为未定义。三个函数分别用于unsigned int，unsigned long以及unsigned long long。</p>
<h4 id="实现"><a href="#实现" class="headerlink" title="实现"></a><strong>实现</strong></h4><figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_ctzl(<span class="keyword">unsigned</span> <span class="keyword">long</span> x) &#123;</span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i != <span class="number">64</span>; ++i)</span><br><span class="line">        <span class="keyword">if</span> (x &gt;&gt; i &amp; <span class="number">1</span>) <span class="keyword">return</span> i;</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_ctzl(<span class="keyword">unsigned</span> <span class="keyword">long</span> x) &#123;</span><br><span class="line">    <span class="keyword">int</span> r = <span class="number">63</span>;</span><br><span class="line">    x &amp;= ~x + <span class="number">1</span>;</span><br><span class="line">    <span class="keyword">if</span> (x &amp; <span class="number">0x00000000FFFFFFFF</span>) r -= <span class="number">32</span>;</span><br><span class="line">    <span class="keyword">if</span> (x &amp; <span class="number">0x0000FFFF0000FFFF</span>) r -= <span class="number">16</span>;</span><br><span class="line">    <span class="keyword">if</span> (x &amp; <span class="number">0x00FF00FF00FF00FF</span>) r -= <span class="number">8</span>;</span><br><span class="line">    <span class="keyword">if</span> (x &amp; <span class="number">0x0F0F0F0F0F0F0F0F</span>) r -= <span class="number">4</span>;</span><br><span class="line">    <span class="keyword">if</span> (x &amp; <span class="number">0x3333333333333333</span>) r -= <span class="number">2</span>;</span><br><span class="line">    <span class="keyword">if</span> (x &amp; <span class="number">0x5555555555555555</span>) r -= <span class="number">1</span>;</span><br><span class="line">    <span class="keyword">return</span> r;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<h3 id="2、-builtin-clz"><a href="#2、-builtin-clz" class="headerlink" title="2、__builtin_clz"></a><strong>2、__builtin_clz</strong></h3><p>&emsp;一共有三个函数，分别适用于不同的输入类型。</p>
<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_clz (<span class="keyword">unsigned</span> <span class="keyword">int</span> x)</span><br><span class="line">Returns the number of leading <span class="number">0</span>-bits in x, starting at the most significant bit position. If x is <span class="number">0</span>, the result is undefined.</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> __builtin_clzl (<span class="keyword">unsigned</span> <span class="keyword">long</span>)</span><br><span class="line">Similar to __builtin_clz, except the argument type is <span class="keyword">unsigned</span> <span class="keyword">long</span>.</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> __builtin_clzll (<span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span>)</span><br><span class="line">Similar to __builtin_clz, except the argument type is <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span>.</span><br></pre></td></tr></table></figure>
<p>&emsp;这个函数作用是返回输入数二进制表示从最高位开始(左起)的连续的0的个数；如果传入0则行为未定义。三个不同的函数分别用于unsigned int，unsigned long以及unsigned long long。</p>
<h4 id="实现-1"><a href="#实现-1" class="headerlink" title="实现"></a><strong>实现</strong></h4><figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_clzl(<span class="keyword">unsigned</span> <span class="keyword">long</span> x) &#123;</span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i != <span class="number">64</span>; ++i)</span><br><span class="line">        <span class="keyword">if</span> (x &gt;&gt; <span class="number">63</span> - i &amp; <span class="number">1</span>) </span><br><span class="line">            <span class="keyword">return</span> i;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_clzl(<span class="keyword">unsigned</span> <span class="keyword">long</span> x) &#123;</span><br><span class="line">    <span class="keyword">int</span> r = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">if</span> (!(x &amp; <span class="number">0xFFFFFFFF00000000</span>)) r += <span class="number">32</span>, x &lt;&lt;= <span class="number">32</span>;</span><br><span class="line">    <span class="keyword">if</span> (!(x &amp; <span class="number">0xFFFF000000000000</span>)) r += <span class="number">16</span>, x &lt;&lt;= <span class="number">16</span>;</span><br><span class="line">    <span class="keyword">if</span> (!(x &amp; <span class="number">0xFF00000000000000</span>)) r += <span class="number">8</span>,  x &lt;&lt;= <span class="number">8</span>;</span><br><span class="line">    <span class="keyword">if</span> (!(x &amp; <span class="number">0xF000000000000000</span>)) r += <span class="number">4</span>,  x &lt;&lt;= <span class="number">4</span>;</span><br><span class="line">    <span class="keyword">if</span> (!(x &amp; <span class="number">0xC000000000000000</span>)) r += <span class="number">2</span>,  x &lt;&lt;= <span class="number">2</span>;</span><br><span class="line">    <span class="keyword">if</span> (!(x &amp; <span class="number">0x8000000000000000</span>)) r += <span class="number">1</span>,  x &lt;&lt;= <span class="number">1</span>;</span><br><span class="line">    <span class="keyword">return</span> r;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<h3 id="3、-builtin-ffs"><a href="#3、-builtin-ffs" class="headerlink" title="3、__builtin_ffs"></a><strong>3、__builtin_ffs</strong></h3><p>&emsp;一共有三个函数，分别适用于不同的输入类型。</p>
<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_ffs (<span class="keyword">unsigned</span> <span class="keyword">int</span> x)</span><br><span class="line">Returns one plus the index of the least significant <span class="number">1</span>-bit of x, <span class="keyword">or</span> <span class="keyword">if</span> x is zero, returns zero.</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> __builtin_ffsl (<span class="keyword">unsigned</span> <span class="keyword">long</span>)</span><br><span class="line">Similar to __builtin_ffs, except the argument type is <span class="keyword">unsigned</span> <span class="keyword">long</span>.</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> __builtin_ffsll (<span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span>)</span><br><span class="line">Similar to __builtin_ffs, except the argument type is <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span>.</span><br></pre></td></tr></table></figure>
<p>&emsp;这个函数作用是返回输入数二进制表示的最低非0位的下标，下标从1开始计数；如果传入0则返回0。三个不同的函数分别用于unsigned int，unsigned long以及unsigned long long。</p>
<h4 id="实现-2"><a href="#实现-2" class="headerlink" title="实现"></a><strong>实现</strong></h4><p>&emsp;除输入0以外，满足 __builtin_ffs(x) = __builtin_ctz(x) + 1 。</p>
<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_clzl(<span class="keyword">unsigned</span> <span class="keyword">long</span> x) &#123;</span><br><span class="line">    <span class="keyword">if</span> (x == <span class="number">0</span>) <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">return</span> __builtin_ctz(x) + <span class="number">1</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<h3 id="4、-bulitin-popcount"><a href="#4、-bulitin-popcount" class="headerlink" title="4、__bulitin_popcount"></a><strong>4、__bulitin_popcount</strong></h3><p>&emsp;一共有三个函数，分别适用于不同的输入类型。</p>
<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_popcount (<span class="keyword">unsigned</span> <span class="keyword">int</span> x)</span><br><span class="line">Returns the number of <span class="number">1</span>-bits in x.</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> __builtin_popcountl (<span class="keyword">unsigned</span> <span class="keyword">long</span>)</span><br><span class="line">Similar to __builtin_popcount, except the argument type is <span class="keyword">unsigned</span> <span class="keyword">long</span>.</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> __builtin_popcountll (<span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span>)</span><br><span class="line">Similar to __builtin_popcount, except the argument type is <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span>.</span><br></pre></td></tr></table></figure>
<p>&emsp;这个函数作用是返回输入的二进制表示中1的个数；如果传入0则返回 0 。三个不同的函数分别用于unsigned int，unsigned long以及unsigned long long。</p>
<h4 id="实现-3"><a href="#实现-3" class="headerlink" title="实现"></a><strong>实现</strong></h4><figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_popcountl(<span class="keyword">unsigned</span> <span class="keyword">long</span> x) &#123;</span><br><span class="line">    <span class="keyword">int</span> r = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">do</span>&#123;</span><br><span class="line">        r += x &amp; <span class="number">1</span>;</span><br><span class="line">    <span class="keyword">while</span> (x &gt;&gt;= <span class="number">1</span>);</span><br><span class="line">    <span class="keyword">return</span> r;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_popcountl(<span class="keyword">unsigned</span> <span class="keyword">long</span> x) &#123;</span><br><span class="line">    <span class="keyword">int</span> r = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">for</span> (; x; x &amp;= x - <span class="number">1</span>) ++r;</span><br><span class="line">    <span class="keyword">return</span> r;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_popcountl(<span class="keyword">unsigned</span> <span class="keyword">long</span> x) &#123;</span><br><span class="line">    x = (x &amp; <span class="number">0x5555555555555555</span>) + (x &gt;&gt; <span class="number">1</span>  &amp; <span class="number">0x5555555555555555</span>);</span><br><span class="line">    x = (x &amp; <span class="number">0x3333333333333333</span>) + (x &gt;&gt; <span class="number">2</span>  &amp; <span class="number">0x3333333333333333</span>);</span><br><span class="line">    x = (x &amp; <span class="number">0x0F0F0F0F0F0F0F0F</span>) + (x &gt;&gt; <span class="number">4</span>  &amp; <span class="number">0x0F0F0F0F0F0F0F0F</span>);</span><br><span class="line">    x = (x &amp; <span class="number">0x00FF00FF00FF00FF</span>) + (x &gt;&gt; <span class="number">8</span>  &amp; <span class="number">0x00FF00FF00FF00FF</span>);</span><br><span class="line">    x = (x &amp; <span class="number">0x0000FFFF0000FFFF</span>) + (x &gt;&gt; <span class="number">16</span> &amp; <span class="number">0x0000FFFF0000FFFF</span>);</span><br><span class="line">    x = (x &amp; <span class="number">0x00000000FFFFFFFF</span>) + (x &gt;&gt; <span class="number">32</span> &amp; <span class="number">0x00000000FFFFFFFF</span>);</span><br><span class="line">    <span class="keyword">return</span> x;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_popcountl(<span class="keyword">unsigned</span> <span class="keyword">long</span> x) &#123;</span><br><span class="line">    x -= (x &gt;&gt; <span class="number">1</span>) &amp; <span class="number">0x5555555555555555</span>;</span><br><span class="line">    x = (x &amp; <span class="number">0x3333333333333333</span>) + (x &gt;&gt; <span class="number">2</span> &amp; <span class="number">0x3333333333333333</span>);</span><br><span class="line">    x = x + (x &gt;&gt; <span class="number">4</span>) &amp; <span class="number">0x0F0F0F0F0F0F0F0F</span>;</span><br><span class="line">    <span class="keyword">return</span> x * <span class="number">0x0101010101010101</span> &gt;&gt; <span class="number">56</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h3 id="5、-bulitin-popcount"><a href="#5、-bulitin-popcount" class="headerlink" title="5、__bulitin_popcount"></a><strong>5、__bulitin_popcount</strong></h3><p>&emsp;一共有三个函数，分别适用于不同的输入类型。</p>
<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_parity (<span class="keyword">unsigned</span> <span class="keyword">int</span> x)</span><br><span class="line">Returns the parity of x, i.e. the number of <span class="number">1</span>-bits in x modulo <span class="number">2.</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> __builtin_parityl (<span class="keyword">unsigned</span> <span class="keyword">long</span>)</span><br><span class="line">Similar to __builtin_parity, except the argument type is <span class="keyword">unsigned</span> <span class="keyword">long</span>.</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> __builtin_parityll (<span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span>)</span><br><span class="line">Similar to __builtin_parity, except the argument type is <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span>.</span><br></pre></td></tr></table></figure>
<p>&emsp;这个函数作用是返回输入的二进制表示中1的个数的奇偶,也就是输入的二进制中1的个数对2取模的结果。三个不同的函数分别用于unsigned int，unsigned long以及unsigned long long。</p>
<h4 id="实现-4"><a href="#实现-4" class="headerlink" title="实现"></a><strong>实现</strong></h4><p>&emsp;根据定义，等价于__builtin_popcount(x) &amp; 1 。</p>
<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_parityl(<span class="keyword">unsigned</span> <span class="keyword">long</span> x) &#123;</span><br><span class="line">    <span class="keyword">return</span> __builtin_popcountl(x) &amp; <span class="number">1</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="keyword">int</span> __builtin_parityl(<span class="keyword">unsigned</span> <span class="keyword">long</span> x) &#123;</span><br><span class="line">    x ^= x &gt;&gt; <span class="number">1</span>;</span><br><span class="line">    x ^= x &gt;&gt; <span class="number">2</span>;</span><br><span class="line">    x ^= x &gt;&gt; <span class="number">4</span>;</span><br><span class="line">    x ^= x &gt;&gt; <span class="number">8</span>;</span><br><span class="line">    x ^= x &gt;&gt; <span class="number">16</span>;</span><br><span class="line">    x ^= x &gt;&gt; <span class="number">32</span>;</span><br><span class="line">    <span class="keyword">return</span> x &amp; <span class="number">1</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<p>&emsp;这几个函数中都有很巧妙的位运算，大大降低了复杂度。关于位运算的更多例子，可以参考链接<a target="_blank" rel="noopener" href="http://graphics.stanford.edu/~seander/bithacks.html"> [4] </a>。</p>
<p>[1]<a target="_blank" rel="noopener" href="https://gcc.gnu.org/onlinedocs/gcc-4.3.2/gcc/Other-Builtins.html#Other-Builtins">https://gcc.gnu.org/onlinedocs/gcc-4.3.2/gcc/Other-Builtins.html#Other-Builtins</a><br>[2]<a target="_blank" rel="noopener" href="https://www.cnblogs.com/justinh/p/7754655.html">https://www.cnblogs.com/justinh/p/7754655.html</a><br>[3]<a target="_blank" rel="noopener" href="https://xr1s.me/2018/08/23/gcc-builtin-implementation/">https://xr1s.me/2018/08/23/gcc-builtin-implementation/</a><br>[4]<a target="_blank" rel="noopener" href="http://graphics.stanford.edu/~seander/bithacks.html">http://graphics.stanford.edu/~seander/bithacks.html</a></p>
</article><div class="post-copyright"><div class="post-copyright__author"><span class="post-copyright-meta">文章作者: </span><span class="post-copyright-info"><a href="mailto:undefined">Tom</a></span></div><div class="post-copyright__type"><span class="post-copyright-meta">文章链接: </span><span class="post-copyright-info"><a href="https://tomsworkspace.github.io/2021/02/27/GCC%E8%87%AA%E5%B8%A6%E7%9A%84%E4%B8%80%E4%BA%9Bbuiltin%E5%86%85%E5%BB%BA%E5%87%BD%E6%95%B0/">https://tomsworkspace.github.io/2021/02/27/GCC%E8%87%AA%E5%B8%A6%E7%9A%84%E4%B8%80%E4%BA%9Bbuiltin%E5%86%85%E5%BB%BA%E5%87%BD%E6%95%B0/</a></span></div><div class="post-copyright__notice"><span class="post-copyright-meta">版权声明: </span><span class="post-copyright-info">本博客所有文章除特别声明外，均采用 <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/" target="_blank">CC BY-NC-SA 4.0</a> 许可协议。转载请注明来自 <a href="https://TOMsworkspace.github.io" target="_blank">Tom's develop Blog</a>！</span></div></div><div class="tag_share"><div class="post-meta__tag-list"><a class="post-meta__tags" href="/tags/GCC/">GCC</a><a class="post-meta__tags" href="/tags/bulitin%E5%87%BD%E6%95%B0/">bulitin函数</a></div><div class="post_share"><div class="social-share" data-image="https://cdn.jsdelivr.net/gh/TOMsworkspace/TOMsworkspace.github.io/2021/02/27/GCC自带的一些builtin内建函数/figure1.jpg" data-sites="facebook,twitter,wechat,weibo,qq"></div><link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/social-share.js/dist/css/share.min.css"><script src="https://cdn.jsdelivr.net/npm/social-share.js/dist/js/social-share.min.js" defer></script></div></div><div class="post-reward"><div class="reward-button"><i class="fas fa-qrcode"></i> 打赏<div class="reward-main"><ul class="reward-all"><li class="reward-item"><a href="https://cdn.jsdelivr.net/gh/TOMsworkspace/BlogHelper@1.0/wp.jpg" target="_blank"><img class="post-qr-code-img" data-lazy-src="https://cdn.jsdelivr.net/gh/TOMsworkspace/BlogHelper@1.0/wp.jpg" alt="wechat"/></a><div class="post-qr-code-desc">wechat</div></li></ul></div></div></div><nav class="pagination-post" id="pagination"><div class="prev-post pull-left"><a href="/2021/03/03/C++%E4%B8%AD%E7%9A%84%E6%8C%87%E9%92%88%E4%B8%8E%E5%BC%95%E7%94%A8/"><img class="prev-cover" data-lazy-src="https://cdn.jsdelivr.net/gh/TOMsworkspace/TOMsworkspace.github.io/2021/03/03/C++中的指针与引用/figure1.jpg" onerror="onerror=null;src='/img/404.jpg'"><div class="pagination-info"><div class="label">上一篇</div><div class="prev_info">C++中的指针与引用</div></div></a></div><div class="next-post pull-right"><a href="/2021/02/25/C++%E4%B8%ADconst%E5%8F%98%E9%87%8F%E7%9A%84%E4%BF%AE%E6%94%B9%E4%B8%8E%E8%B5%8B%E5%80%BC/"><img class="next-cover" data-lazy-src="https://cdn.jsdelivr.net/gh/TOMsworkspace/TOMsworkspace.github.io/2021/02/25/C++中const变量的修改与赋值/figure1.jpg" onerror="onerror=null;src='/img/404.jpg'"><div class="pagination-info"><div class="label">下一篇</div><div class="next_info">C++中const变量的修改与赋值</div></div></a></div></nav><hr/><div id="post-comment"><div class="comment-head"><div class="comment-headline"><i class="fas fa-comments fa-fw"></i><span> 评论</span></div></div><div class="comment-wrap"><div><div id="gitalk-container"></div></div></div></div></div><div class="aside_content" id="aside_content"><div class="card-widget card-info"><div class="card-content"><div class="card-info-avatar is-center"><img class="avatar-img" data-lazy-src="https://cdn.jsdelivr.net/gh/TOMsworkspace/BlogHelper@1.0/avator.jpg" onerror="this.onerror=null;this.src='/img/friend_404.gif'" alt="avatar"/><div class="author-info__name">Tom</div><div class="author-info__description">keep curiously!</div></div><div class="card-info-data"><div class="card-info-data-item is-center"><a href="/archives/"><div class="headline">文章</div><div class="length-num">38</div></a></div><div class="card-info-data-item is-center"><a href="/tags/"><div class="headline">标签</div><div class="length-num">73</div></a></div><div class="card-info-data-item is-center"><a href="/categories/"><div class="headline">分类</div><div class="length-num">12</div></a></div></div><a class="button--animated" id="card-info-btn" target="_blank" rel="noopener" href="https://github.com/TOMsworkspace"><i class="fab fa-github"></i><span>Follow Me</span></a><div class="card-info-social-icons is-center"><a class="social-icon" href="https://github.com/TOMsworkspace" target="_blank" title="Github"><i class="fab fa-github"></i></a><a class="social-icon" href="mailto:cqucscw@gmail.com" target="_blank" title="Email"><i class="fas fa-envelope"></i></a></div></div></div><div class="card-widget card-announcement"><div class="card-content"><div class="item-headline"><i class="fas fa-bullhorn card-announcement-animation"></i><span>公告</span></div><div class="announcement_content">This is my Blog</div></div></div><div class="sticky_layout"><div class="card-widget" id="card-toc"><div class="card-content"><div class="item-headline"><i class="fas fa-stream"></i><span>目录</span></div><div class="toc-content"><ol class="toc"><li class="toc-item toc-level-2"><a class="toc-link" href="#%E4%B8%80%E3%80%81GCC%E5%86%85%E5%BB%BA%E5%87%BD%E6%95%B0"><span class="toc-number">1.</span> <span class="toc-text">一、GCC内建函数</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E4%BA%8C%E3%80%81%E5%B8%B8%E7%94%A8%E7%9A%84%E5%86%85%E5%BB%BA%E5%87%BD%E6%95%B0%E5%8F%8A%E5%AE%9E%E7%8E%B0"><span class="toc-number">2.</span> <span class="toc-text">二、常用的内建函数及实现</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#1%E3%80%81-builtin-ctz"><span class="toc-number">2.1.</span> <span class="toc-text">1、__builtin_ctz</span></a><ol class="toc-child"><li class="toc-item toc-level-4"><a class="toc-link" href="#%E5%AE%9E%E7%8E%B0"><span class="toc-number">2.1.1.</span> <span class="toc-text">实现</span></a></li></ol></li><li class="toc-item toc-level-3"><a class="toc-link" href="#2%E3%80%81-builtin-clz"><span class="toc-number">2.2.</span> <span class="toc-text">2、__builtin_clz</span></a><ol class="toc-child"><li class="toc-item toc-level-4"><a class="toc-link" href="#%E5%AE%9E%E7%8E%B0-1"><span class="toc-number">2.2.1.</span> <span class="toc-text">实现</span></a></li></ol></li><li class="toc-item toc-level-3"><a class="toc-link" href="#3%E3%80%81-builtin-ffs"><span class="toc-number">2.3.</span> <span class="toc-text">3、__builtin_ffs</span></a><ol class="toc-child"><li class="toc-item toc-level-4"><a class="toc-link" href="#%E5%AE%9E%E7%8E%B0-2"><span class="toc-number">2.3.1.</span> <span class="toc-text">实现</span></a></li></ol></li><li class="toc-item toc-level-3"><a class="toc-link" href="#4%E3%80%81-bulitin-popcount"><span class="toc-number">2.4.</span> <span class="toc-text">4、__bulitin_popcount</span></a><ol class="toc-child"><li class="toc-item toc-level-4"><a class="toc-link" href="#%E5%AE%9E%E7%8E%B0-3"><span class="toc-number">2.4.1.</span> <span class="toc-text">实现</span></a></li></ol></li><li class="toc-item toc-level-3"><a class="toc-link" href="#5%E3%80%81-bulitin-popcount"><span class="toc-number">2.5.</span> <span class="toc-text">5、__bulitin_popcount</span></a><ol class="toc-child"><li class="toc-item toc-level-4"><a class="toc-link" href="#%E5%AE%9E%E7%8E%B0-4"><span class="toc-number">2.5.1.</span> <span class="toc-text">实现</span></a></li></ol></li></ol></li></ol></div></div></div><div class="card-widget card-recent-post"><div class="card-content"><div class="item-headline"><i class="fas fa-history"></i><span>最新文章</span></div><div class="aside-list"><div class="aside-list-item"><a class="thumbnail" href="/2021/09/27/%E6%B5%81%E4%BD%93%E6%A8%A1%E6%8B%9F%E4%B8%8ESPH%E6%96%B9%E6%B3%95/" title="流体模拟与SPH方法"><img data-lazy-src="https://cdn.jsdelivr.net/gh/TOMsworkspace/TOMsworkspace.github.io/2021/09/27/流体模拟与SPH方法/figure1.jpg" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="流体模拟与SPH方法"/></a><div class="content"><a class="title" href="/2021/09/27/%E6%B5%81%E4%BD%93%E6%A8%A1%E6%8B%9F%E4%B8%8ESPH%E6%96%B9%E6%B3%95/" title="流体模拟与SPH方法">流体模拟与SPH方法</a><time datetime="2021-09-27T08:46:17.000Z" title="发表于 2021-09-27 16:46:17">2021-09-27</time></div></div><div class="aside-list-item"><a class="thumbnail" href="/2021/09/11/%E5%BC%B9%E6%80%A7%E6%9C%89%E9%99%90%E5%85%83%E6%96%B9%E6%B3%95/" title="弹性有限元方法"><img data-lazy-src="https://cdn.jsdelivr.net/gh/TOMsworkspace/TOMsworkspace.github.io/2021/09/11/弹性有限元方法/figure1.jpg" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="弹性有限元方法"/></a><div class="content"><a class="title" href="/2021/09/11/%E5%BC%B9%E6%80%A7%E6%9C%89%E9%99%90%E5%85%83%E6%96%B9%E6%B3%95/" title="弹性有限元方法">弹性有限元方法</a><time datetime="2021-09-11T09:05:34.000Z" title="发表于 2021-09-11 17:05:34">2021-09-11</time></div></div><div class="aside-list-item"><a class="thumbnail" href="/2021/08/09/%E5%BC%B9%E7%B0%A7%E8%B4%A8%E7%82%B9%E7%B3%BB%E7%BB%9F%E4%B8%8E%E6%97%B6%E9%97%B4%E7%A7%AF%E5%88%86/" title="弹簧质点系统与时间积分"><img data-lazy-src="https://cdn.jsdelivr.net/gh/TOMsworkspace/TOMsworkspace.github.io/2021/08/09/弹簧质点系统与时间积分/figure1.png" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="弹簧质点系统与时间积分"/></a><div class="content"><a class="title" href="/2021/08/09/%E5%BC%B9%E7%B0%A7%E8%B4%A8%E7%82%B9%E7%B3%BB%E7%BB%9F%E4%B8%8E%E6%97%B6%E9%97%B4%E7%A7%AF%E5%88%86/" title="弹簧质点系统与时间积分">弹簧质点系统与时间积分</a><time datetime="2021-08-09T13:39:12.000Z" title="发表于 2021-08-09 21:39:12">2021-08-09</time></div></div><div class="aside-list-item"><a class="thumbnail" href="/2021/08/08/OpenGL%E5%9D%90%E6%A0%87%E7%B3%BB%E7%BB%9F/" title="OpenGL坐标系统"><img data-lazy-src="https://cdn.jsdelivr.net/gh/TOMsworkspace/TOMsworkspace.github.io/2021/08/08/OpenGL坐标系统/figure1.png" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="OpenGL坐标系统"/></a><div class="content"><a class="title" href="/2021/08/08/OpenGL%E5%9D%90%E6%A0%87%E7%B3%BB%E7%BB%9F/" title="OpenGL坐标系统">OpenGL坐标系统</a><time datetime="2021-08-08T12:57:28.000Z" title="发表于 2021-08-08 20:57:28">2021-08-08</time></div></div><div class="aside-list-item"><a class="thumbnail" href="/2021/08/06/Doxygen%E8%87%AA%E5%8A%A8%E7%94%9F%E6%88%90%E6%96%87%E6%A1%A3/" title="Doxygen自动生成文档"><img data-lazy-src="https://cdn.jsdelivr.net/gh/TOMsworkspace/TOMsworkspace.github.io/2021/08/06/Doxygen自动生成文档/Doxygen.png" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="Doxygen自动生成文档"/></a><div class="content"><a class="title" href="/2021/08/06/Doxygen%E8%87%AA%E5%8A%A8%E7%94%9F%E6%88%90%E6%96%87%E6%A1%A3/" title="Doxygen自动生成文档">Doxygen自动生成文档</a><time datetime="2021-08-06T13:24:50.000Z" title="发表于 2021-08-06 21:24:50">2021-08-06</time></div></div></div></div></div></div></div></main><footer id="footer"><div id="footer-wrap"><div class="copyright">&copy;2019 - 2021 By Tom</div><div class="framework-info"><span>框架 </span><a target="_blank" rel="noopener" href="https://hexo.io">Hexo</a><span class="footer-separator">|</span><span>主题 </span><a target="_blank" rel="noopener" href="https://github.com/jerryc127/hexo-theme-butterfly">Butterfly</a></div><div class="footer_custom_text">Hi, welcome to my <a href="https://TOMsworkspace.github.io/">blog</a>!</div></div></footer></div><div id="rightside"><div id="rightside-config-hide"><button id="readmode" type="button" title="阅读模式"><i class="fas fa-book-open"></i></button><button id="translateLink" type="button" title="简繁转换">简</button><button id="darkmode" type="button" title="浅色和深色模式转换"><i class="fas fa-adjust"></i></button></div><div id="rightside-config-show"><button id="rightside_config" type="button" title="设置"><i class="fas fa-cog"></i></button><button id="chat_btn" type="button" title="rightside.chat_btn"><i class="fas fa-sms"></i></button><a id="to_comment" href="#post-comment" title="直达评论"><i class="fas fa-comments"></i></a><button id="go-up" type="button" title="回到顶部"><i class="fas fa-arrow-up"></i></button></div></div><div><script src="https://cdn.jsdelivr.net/npm/jquery@latest/dist/jquery.min.js"></script><script src="/js/utils.js"></script><script src="/js/main.js"></script><script src="/js/tw_cn.js"></script><script src="https://cdn.jsdelivr.net/npm/medium-zoom/dist/medium-zoom.min.js"></script><script src="https://cdn.jsdelivr.net/npm/instant.page/instantpage.min.js" type="module" defer></script><script src="https://cdn.jsdelivr.net/npm/vanilla-lazyload/dist/lazyload.iife.min.js"></script><div class="js-pjax"><script>if (!window.MathJax) {
  window.MathJax = {
    loader: {
      source: {
        '[tex]/amsCd': '[tex]/amscd'
      }
    },
    tex: {
      inlineMath: [ ['$','$'], ["\\(","\\)"]],
      tags: 'ams'
    },
    options: {
      renderActions: {
        findScript: [10, doc => {
          for (const node of document.querySelectorAll('script[type^="math/tex"]')) {
            const display = !!node.type.match(/; *mode=display/)
            const math = new doc.options.MathItem(node.textContent, doc.inputJax[0], display)
            const text = document.createTextNode('')
            node.parentNode.replaceChild(text, node)
            math.start = {node: text, delim: '', n: 0}
            math.end = {node: text, delim: '', n: 0}
            doc.math.push(math)
          }
        }, ''],
        addClass: [200,() => {
          document.querySelectorAll('mjx-container:not([display=\'true\']').forEach( node => {
            const target = node.parentNode
            if (!target.classList.contains('has-jax')) {
              target.classList.add('mathjax-overflow')
            }
          })
        }, '', false]
      }
    }
  }
  
  const script = document.createElement('script')
  script.src = 'https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js'
  script.id = 'MathJax-script'
  script.async = true
  document.head.appendChild(script)
} else {
  MathJax.startup.document.state(0)
  MathJax.texReset()
  MathJax.typeset()
}</script><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.css"><script src="https://cdn.jsdelivr.net/npm/katex-copytex@latest/dist/katex-copytex.min.js"></script><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex-copytex@latest/dist/katex-copytex.min.css"><script>$(function () {
  $('span.katex-display').wrap('<div class="katex-wrap"></div>')
})</script><script>function addGitalkSource () {
  const ele = document.createElement('link')
  ele.rel = 'stylesheet'
  ele.href= 'https://cdn.jsdelivr.net/npm/gitalk/dist/gitalk.min.css'
  document.getElementsByTagName('head')[0].appendChild(ele)
}

function loadGitalk () {
  function initGitalk () {
    var gitalk = new Gitalk({
      clientID: 'e50742231659674c31e3',
      clientSecret: '59038139e289bc384e484d341205bbb95a123209',
      repo: 'TOMsworkspace.github.io',
      owner: 'TOMsworkspace',
      admin: ['TOMsworkspace'],
      id: '1e100c61ce64bc938e6fe9796e39f1b9',
      language: '-zh-CN# en, zh-CN, zh-TW, es-ES, fr, ru',
      perPage: 10,
      distractionFreeMode: false,
      pagerDirection: 'last',
      createIssueManually: true,
      updateCountCallback: commentCount
    })
    gitalk.render('gitalk-container')
  }

  if (typeof Gitalk === 'function') initGitalk()
  else {
    addGitalkSource()
    $.getScript('https://cdn.jsdelivr.net/npm/gitalk@latest/dist/gitalk.min.js', initGitalk)
  }
}

function commentCount(n){
  let isCommentCount = document.querySelector('#post-meta .gitalk-comment-count')
  if (isCommentCount) {
    isCommentCount.innerHTML= n
  }
}

if ('Gitalk' === 'Gitalk' || !false) {
  if (false) btf.loadComment(document.getElementById('gitalk-container'), loadGitalk)
  else loadGitalk()
} else {
  function loadOtherComment () {
    loadGitalk()
  }
}</script><script async src="//busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script></div><script defer="defer" id="fluttering_ribbon" mobile="false" src="https://cdn.jsdelivr.net/npm/butterfly-extsrc@1/dist/canvas-fluttering-ribbon.min.js"></script><script id="click-show-text" src="https://cdn.jsdelivr.net/npm/butterfly-extsrc@1/dist/click-show-text.min.js" async="async" mobile="false"></script><script>(function(){
  const bp = document.createElement('script');
  const curProtocol = window.location.protocol.split(':')[0];
  if (curProtocol === 'https'){
  bp.src = 'https://zz.bdstatic.com/linksubmit/push.js';
  }
  else{
  bp.src = 'http://push.zhanzhang.baidu.com/push.js';
  }
  bp.dataset.pjax = ''
  const s = document.getElementsByTagName("script")[0];
  s.parentNode.insertBefore(bp, s);
})()</script></div></body></html>